The statistical physics of cities


Challenges due to the rapid urbanization of the world — especially in emerging countries — range from an increasing dependence on energy to air pollution, socio-spatial inequalities and environmental and sustainability issues. Modelling the structure and evolution of cities is therefore critical because policy makers need robust theories and new paradigms for mitigating these problems. Fortunately, the increased data available about urban systems opens the possibility of constructing a quantitative ‘science of cities’, with the aim of identifying and modelling essential phenomena. Statistical physics plays a major role in this effort by bringing tools and concepts able to bridge theory and empirical results. This Perspective illustrates this point by focusing on fundamental objects in cities: the distribution of the urban population; segregation phenomena and spin-like models; the polycentric transition of the activity organization; energy considerations about mobility and models inspired by gravity and radiation concepts; CO2 emitted by transport; and finally, scaling that describes how various socio-economical and infrastructures evolve when cities grow.

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Fig. 1: Equilibrium configurations at zero temperature for cities with collective or selfish dynamics.
Fig. 2: Effective speed in human mobility as a function of travel distance.
Fig. 3: Scaling of quantities with city population may depend on the definition of a city.
Fig. 4: Carbon footprint (in millions of tonnes of CO2) versus population for various urban areas.


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Barthelemy, M. The statistical physics of cities. Nat Rev Phys 1, 406–415 (2019).

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